System and method for dynamically calibrating and measuring analyte concentration in diabetes management monitors

ABSTRACT

An optical analyte sensor and diabetes management system is provided. The sensor preferably includes a hydrogel matrix for receiving a sample containing an analyte at unknown concentration, a light emitter for emitting light at a stimulation frequency, a light receiver for receiving a fluorescence signal at a first isosbestic frequency, and at a second frequency, for measuring an intensity of the fluorescence signal and the first and second frequencies. A processor determines a concentration of the analyte based on the respective intensities.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.14/448,867, filed Jul. 31, 2014, which claims priority under 35 U.S.C. §119(e) to provisional application No. 61/921,309, filed Dec. 27, 2013,the entire contents of which are hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to systems and methods for monitoringanalytes. More particularly, the present invention relates to systemsand methods for dynamically calibrating and measuring analyteconcentration in diabetes management systems, such as continuous glucosemonitors using a fluorescence signal at an analyte concentrationindependent wavelength.

BACKGROUND OF THE INVENTION

Diabetes is a group of diseases marked by high levels of blood glucoseresulting from defects in insulin production, insulin action, or both.There are 23.6 million people in the United States, or 8% of thepopulation, who have diabetes. The total prevalence of diabetes hasincreased 13.5% since the 2005-2007 time period. Diabetes can lead toserious complications and premature death, but there are well-knownproducts available for people with diabetes to help control the diseaseand lower the risk of complications. Chronic hyperglycemia leads toserious sometimes irreversible complications including renal failure,peripheral neuropathy, retinopathy, and vascular system complications.

Treatment options for people with diabetes include specialized diets,oral medications and/or insulin therapy. The primary goal for diabetestreatment is to control the patient's blood glucose (sugar) level inorder to increase the chances of a complication-free life.

Glycemic control of patients afflicted with Type 1 or Type 2 diabetesmellitus is essential to minimize acute and chronic effects ofhypoglycemia or hyperglycemia. Utilization of continuous glucosemonitoring (CGM) as a means to measure effectiveness of treatmentsfocuses on attaining glycemic control was first introduced intocommercial use over ten years ago. Since that time, CGM's have beenincorporated into insulin pumps which automatically infuse insulin whenblood sugar levels are measured by the CGM to be above threshold levelschosen by the patient after consultation with their physician.

Glucose sensors are an essential element in diabetes management. Inparticular, continuous glucose sensors provide numerous advantages overepisodic glucose sensors or conventional finger-stick glucose teststrips. Artificial pancreas architectures rely on accurate continuousglucose measurements.

Many existing CGM's are presently based on glucose oxidase. Morerecently, however, Becton, Dickinson and Company has demonstrated a CGMbased on a fluorescently labeled glucose binding protein (GBP) containedin a glucose-permeable hydrogel matrix. The glucose binding proteinundergoes a conformational change in the presence of glucose, whichaffects the fluorescence intensity. Accordingly fluorescence emissionspectra may be used to determine glucose concentration continuously. Onedifficulty with fluorescence measuring systems is due to the inherentlynoisy nature of optical intensity signals. Another problem with CGMdevices is with initial calibration, and maintaining calibration overthe life of the sensor, to ensure accurate glucose measurements.Accordingly, there is a need for a CGM that is capable ofself-calibration and dynamic calibration during use, in order to improvethe speed and accuracy of glucose measurements. Although embodimentsdescribed herein discuss a GBP contained in a matrix, it should beappreciated that any suitable substance or compound may be containedwithin the matrix. Embodiments of the present invention are not limitedto matrices containing a GBP, and in particular, may include withoutlimitation boronic acid or any glucose binding compound. In addition, itshould be understood that embodiments of the present invention may bedeployed to any suitable location of a host, including withoutlimitation subcutaneous, intradermal, supradermal, and intravascularspace. Further, it should be understood that embodiments of the presentinvention may be deployed within or utilizing any bodily fluid,including without limitation, blood, urine, interstitial fluid, lymphfluid and tears.

SUMMARY OF THE INVENTION

Exemplary embodiments of the present invention address at least theabove described problems and/or disadvantages and provide at least theadvantages described below. Accordingly, it is an object of certainembodiments of the present invention to provide an optical analytesensor for determining a concentration of an analyte. The sensorcomprises a matrix for receiving a sample containing the analyte at anunknown concentration. The sensor comprises a light emitted for emittinglight at a stimulation frequency upon the sample. A light receiverreceives a fluorescence signal at a first isosbestic frequency, and at asecond frequency, for measuring an intensity of the fluorescence signalat the first and second frequency. A processor determines aconcentration of the analyte based on the respective intensitiesmeasured at the first and second frequencies.

Another exemplary embodiment of the invention provides a diabetesmanagement system comprising an optical analyte sensor and an insulininfusion device. The optical analyte sensor comprises a matrix forreceiving a sample containing the analyte at an unknown concentrationand a light emitter for emitting light at a stimulation frequency uponthe sample. The sensor further comprises a light receiver for receivinga fluorescence signal at a first isosbestic frequency, and at a secondfrequency, and for measuring an intensity of the fluorescence signal atthe first and second frequencies. A processor determines a concentrationof the analyte based on the respective intensities measured at the firstand second frequencies. The sensor further comprises a transceiver fortransmitting a signal to the insulin infusion device.

Yet another exemplary embodiment of the present invention provides anoptical analyte sensor. The sensor comprises a matrix for receiving asample containing the analyte at an unknown concentration and a lightemitter for emitting light at a stimulation frequency upon the sample.The sensor further comprises a light receiver for receiving afluorescence signal at a first isosbestic frequency, and at a secondfrequency, and for measuring an intensity of the fluorescence signal atthe first and second frequencies. A processor determines a concentrationof the analyte based on the respective intensities measured at the firstand second frequencies. The processor further determines a sensor driftbased on previous intensity measurements and corrects the determinedconcentration based on the determined sensor drift.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other exemplary features and advantages of certainexemplary embodiments of the present invention will become more apparentfrom the following description of certain exemplary embodiments thereofwhen taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a frequency response for a labeled GBP-basedcontinuous glucose sensor having an isosbestic point according to anexemplary embodiment of the present invention;

FIG. 2 illustrates a wavelength at which the spectral density issubstantially independent of glucose concentration according to anexemplary embodiment of the present invention;

FIG. 3 illustrates a comparison between an idealized filter and a realoptical filter model according to an exemplary embodiment of the presentinvention;

FIG. 4 illustrates the change in measured signal strength intensitybetween two states of interest as a function of detection passbandconfigurations according to an exemplary embodiment of the presentinvention; and

FIG. 5 illustrates a block diagram of a calibration process according toan exemplary embodiment of the present invention.

Throughout the drawings, like reference numerals will be understood torefer to like elements, features and structures.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Described herein is a novel system and method for estimating analyteconcentration based on an invariant point in the fluorescence spectra ofthe GBP-acrylodan complex. A desirable analyte to measure is glucose,however, it should be appreciated that embodiments of the presentinvention can estimate the concentration of many different analytesincluding without limitation hemoglobin HbA1c and glycated albumin. An‘isosbestic’ point typically refers to either an absorption or emissionphenomena. Accordingly, the term ‘isosbestic’ as used herein refers tothe analyte-invariant frequency of an emission spectra. As shown in FIG.1, the frequency response for a labeled GBP-based continuous glucosesensor includes an isosbestic point 100. That is, there is a frequencyfor which intensity response is independent of the concentration of thetarget analyte. The isosbestic point is at approximately 520 nm.

The isosbestic point has been used to measure sensor performanceindependent of analyte concentration. This point and the rangeimmediately around it may advantageously be used to dynamicallyself-reference the device and provide robust estimations of glucoselevels. This approach enables a device that can be self-calibrated, anddynamically re-calibrated. An algorithm is provided that is based onphysical models, and allows for more robust design and efficient riskmanagement. Calculation of the estimated glucose concentration mayadvantageously be performed directly at any point in time, rather thanrelying on iterative and cumulative correction factors that are subjectto drift and corruption.

In order for an isosbestic point to be present from an analyte-specificmarker, such as a fluorescently-labeled GBP that enables detection ofglucose, two and only two conformations of the marker need to exist. Oneconformation in the presence of the analyte to be measured and oneconformation in the absence of that analyte. For example, one GBP usedby Becton, Dickinson and Company contains a hinged point around which anopen and closed GBP conformation exists. R. M. de Lorimier, J. J. Smith,M. A. Dwyer, L. L. Looger, K. M. Sali, C. D. Paavola, S. S. Rizk, S.Sadigov, D. W. Conrad, L. Loew, and H. W. Hellinga; Construction of afluorescent biosensor family; Protein Science, (11):2655-2675, 2002. J.C. Pickup, F. Khan, Z.-L. Zhi, J. Coulter, and D. J. S. Birch;Fluorescence intensity- and lifetime-based glucose sensing usingglucose/galactose-binding protein; J Diabetes Sci. Technol., 7(1):62-71,January 2013. K. Weidemaier, A. Lastovich, S. Keith, J. B. Pitner, M.Sistare, R. Jacobson, and D. Kurisko; Multi-day pre-clinicaldemonstration of glucose/galactose binding protein-based fiber opticsensor; Biosensors and Bioelectronics, (26):4117-4123, 2011.

A top-down, event-driven model has been derived. The model is simple andaccurate. Simplicity enables ease of analysis, clarity inimplementation, and reduces the risk of unintended effects due tounnecessary complexity. The model was derived according to the followingprocess. First, initial assumptions were made based on reasonableevidence. Second, an analytical framework was developed that enables thecalculation of an estimated glucose concentration inside the sensor.Third, a process was outlined to implement the findings in a commercialproduct. Fourth, experiments were conducted to collect and analyze datain order to support and/or refine the model, implementation, or processas needed.

A glucose value is converted to a measured signal through a number ofprocess steps, outlined below. The algorithm reverses these steps sothat the original glucose concentration in the sensor may be estimatedaccurately from the signal(s) measured by the device. The illustrativesequence of sensing events is as follows:

1. Glucose enters the sensor;

2. Glucose diffuses through the sensor;

3. Diffusion equilibrium is achieved;

4. Glucose molecules bind to glucose-binding protein molecules (GBP);

5. Bind modifies the fluorescence spectrum;

6. Binding equilibrium is achieved;

7. Light stimulates GBP;

8. GBP fluoresces; and

9. Fluorescence signal leaves sensor and is detected.

In the above process, diffusion, binding, equilibrium, and fluorescenceare concurrent processes. To compute the signal, the sequence isreversed as follows:

1. Detect fluorescence signal;

2. Normalize signal;

3. Determine spectral signature of light;

4. Determine fractional concentration of emission states that createsignature; and

5. Determine concentration of glucose that induces fractionalconcentration states.

The following definitions will be used in the subsequent discussion ofan algorithm for determining glucose concentration.

Configuration Spectra:

σ_(open)(λ)=σ_(open)(λ,[G]=0)

σ_(closed)(λ)=σ_(closed)(λ,[G]=[G]_(saturated)≅[G=∞])

where λ is the optical wavelength, a is the spectral density, [G] is themeasured glucose concentration inside the sensor, and [G]_(saturated)indicates the glucose concentration that will saturate GBP inside thesensor.

${H_{ref}(\lambda)} = {\prod\limits_{i \in \; {{ref}\; {path}}}\; {H_{i}(\lambda)}}$${H_{sig}(\lambda)} = {\prod\limits_{i \in \; {{sig}\; {path}}}\; {H_{i}(\lambda)}}$

where H_(ref) and H_(sig) denote the net optical passbands, H(λ), of thedesired reference and signal channels, respectively. This includes theactual channel filters as well as any filters common to both channels,such as light source, autofluorescence, reflector, and detector transferfunctions.

Fractional Saturation:

Y∈[0,1]=fraction of GBP molecules saturated with glucose

The theory and derivations of the preferred algorithms for determiningglucose concentration according to an exemplary embodiment of thepresent invention will now be discussed. One assumption is that thesystem is substantially in steady-state, meaning the system issubstantially in diffusion equilibrium, chemical (binding) equilibrium,and thermal equilibrium. It should be noted that GBP operates as atwo-state system, where:

n _(open) +n _(closed) =N

such that n is the number of GBP in their respective configurations andN is the number of active GBP in any configuration.

There is a crossing point in the fluorescence spectra of GBP, as shownin FIG. 1, represented by:

${\exists\lambda} = \left. {\lambda_{crosssing} \in \Lambda} \middle| {{{\sigma_{closed}(\lambda)}0}\mspace{11mu} \mspace{14mu} {\frac{d\; \sigma_{open}}{d\; \lambda} \neq \frac{d\; \sigma_{closed}}{d\; \lambda}}} \right.$

where Λ is the optical wavelength range present in the system andσ(λ)>>0 is fulfilled when the amplitude of the crossing is sufficientlyabout the noise level, s_(noise) to be accurately measured:

${SNR}_{dB} = {{20\mspace{14mu} {\log_{10}\left( \frac{\sigma \left( \lambda_{crossing} \right)}{s_{noise}} \right)}}{SNR}_{{dB},\min}}$

The temperature range is preferably below protein denaturation andmelting points. The atomic spectra of the base configurations,σ_(open)(λ) and σ_(closed)(λ), are substantially independent oftemperature in the physiological range:

${\frac{d\; {\sigma (\lambda)}}{dT} \simeq 0},{T \in {{physiological}\mspace{14mu} {range}}}$

Due to the discrete, finite number of binding states and based on theobserved spectra for open and closed configurations of GBP, there is awavelength at which the spectral density is substantially independent ofglucose concentration, as shown in FIG. 2.

A system comprised of N elements, each in one of C configurations, sothat there are n_(i) elements per configuration i, is represented by:

${\sum\limits_{i = 1}^{C}n_{i}} = N$

Each configuration has an optical emission spectral density (‘spectrum’)associated with it:

σ_(i)(λ), i∈{1 . . . C}

Assuming that system elements do not emit coherently, the amplitudes andintensities are additive, such that:

$I_{system} = {{\sum\limits_{j = 1}^{N}I_{j}} = {\sum\limits_{i = 1}^{C}{n_{i}\sigma_{i}}}}$

where I_(#):=n_(#)σ_(#) is the intensity emitted by all elements instate # with spectrum σ_(#).

Combining equations, the spectrum of the system, σ_(system), is aweighted average of each of the constituent spectra:

$\sigma_{system} = {\frac{1}{N}{\sum\limits_{i = 1}^{C}{n_{i}\sigma_{i}}}}$

If there is a wavelength, λ_(crossing), at which spectrum emitted byeach configuration have the same amplitude:

{λ_(crossing)|σ_(i)(λ_(crossing))=σ_(j)(λ_(crossing))}∀i,j∈{1 . . . C}

then it follows that:

$\begin{matrix}{{\sigma_{crossing}\left( \lambda_{crossing} \right)} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}{\sigma_{j}\left( \lambda_{crossing} \right)}}}} \\{= {\frac{1}{N}{\sum\limits_{i = 1}^{C}{n_{i}{\sigma_{i}\left( \lambda_{crossing} \right)}}}}} \\{= {{\sigma_{i}\left( \lambda_{crossing} \right)}\frac{1}{N}{\sum\limits_{i = 1}^{C}n_{i}}}}\end{matrix}$${{and}\mspace{14mu} {since}\text{:}\mspace{11mu} \frac{1}{N}{\sum\limits_{i = 1}^{C}n_{1}}} = {1 = {\sigma_{i}\left( \lambda_{crossing} \right)}}$

Accordingly, there exists a wavelength, λ_(crossing), at which theemitted light intensity is invariant with respect to glucoseconcentration:

σ(λ_(crossing))≠σ(λ_(crossing),[G])

Based on the equations above, there is a range of wavelengths, Λ_(ref),such that the intensity is essentially invariant with respect toglucose, and therefore a reference intensity, I_(ref):

|I _(ref)−χ|=|∫_(Λ) _(ref) σ(λ,[G])dλ−χ|<ε, Λ _(ref)

λ_(crossing), ε>0,∀[G]

where χ is the measured intensity at [G]=0 in a band around the crossingpoint and ε is an acceptable error term.

As GBP is one of two states, n_(open) and n_(closed), the spectrumemitted by the system is a weighted average of its component spectra:

$\begin{matrix}{{\sigma_{system}(\lambda)} = \frac{{n_{open}{\sigma_{open}(\lambda)}} + {n_{closed}{\sigma_{closed}(\lambda)}}}{n_{open} + n_{closed}}} \\{= {{Y\; {\sigma_{closed}(\lambda)}} + {\left( {1 - Y} \right){\sigma_{open}(\lambda)}}}}\end{matrix}$

where Y is the fractional concentration of bound emission states:

$Y:=\frac{n_{closed}}{n_{open} + n_{closed}}$

The measured signal, I, is the power of the fluorescence spectrum overthe detection range:

I=∫ _(Λ)σ(λ)λ⁻² dλ

Because the integration operator is linear and intensities are additivefor incoherent light, the total power of the fluorescence spectrum canbe represented by:

$Y = \frac{{\int_{\Lambda_{sig}}{{\sigma_{total}(\lambda)}\lambda^{- 2}d\; \lambda}} - {\int_{\Lambda_{sig}}{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}}{\int_{\Lambda_{sig}}{\left( {{\sigma_{closed}(\lambda)} - {\sigma_{open}(\lambda)}} \right)\lambda^{- 2}d\; \lambda}}$

If Λ is constrained to the signal range, Λ=Λ_(sig), then solving theabove equation for Y provides:

$\begin{matrix}{I_{total} = {\int{{\sigma_{total}(\lambda)}\lambda^{- 2}d\; \lambda}}} \\{= {{Y{\int{{\sigma_{closed}(\lambda)}\lambda^{- 2}d\; \lambda}}} + {\left( {1 - Y} \right){\int{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}}}} \\{= {{Y\left\lbrack {{\int{{\sigma_{closed}(\lambda)}\lambda^{- 2}d\; \lambda}} - {\int{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}} + \left( {1 - Y} \right)} \right\rbrack} +}} \\{{\int{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}} \\{= {{Y\left\lbrack {\int{\left( {{\sigma_{closed}(\lambda)} - {\sigma_{open}(\lambda)}} \right)\lambda^{- 2}d\; \lambda}} \right\rbrack} +}} \\{{\int{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}}\end{matrix}$

The detected spectra, σ_(sig)(λ) and σ_(ref)(λ), are functions of theoptical filters, H_(sig) and H_(ref), along with the signal andreference paths, respectively.

σ_(sig)(λ)=H _(sig)(λ)·σ_(total)(λ)λ⁻² dλ

σ_(ref)(λ)=H _(ref)(λ)·σ_(total)(λ)λ⁻² dλ

Therefore, the measured light intensities,

I _(sig)=∫_(Λ) H _(sig)(λ)·σ_(total)(λ)λ⁻² dλ

I _(ref)=∫_(Λ) H _(ref)(λ)·σ_(total)(λ)λ⁻² dλ

As discussed above, the reference signal is independent of the glucoseconcentration [G]. Therefore, it can be used as a normalization factorfor all spectral and intensity calculations. This, in turn, allows fordirect comparison and use of any spectra from any device at any time,provided that the fluorescence characteristics of the base states,σ_(open) and σ_(closed), have not been altered. Therefore, allmeasurements of I_(sig) will be normalized by the concurrently measuredvalue of I_(ref).

The values σ_(open), σ_(closed), H_(sig), and H_(ref) are able to becharacterized and recorded prior to deployment of a sensor according toan exemplary embodiment of the present invention. Thus, using the tilde(e.g., {tilde over (σ)}_(open)) to denote recorded values, combining theequations above, and normalizing to I_(ref) yields:

$Y = \frac{{I_{sig} \cdot \frac{1}{I_{ref}} \cdot {\int_{\Lambda}{{{\overset{\sim}{H}}_{ref}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}} - {\int_{\Lambda}{{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}}{\int_{\Lambda}{\left( {{{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{closed}(\lambda)}} - {{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}}} \right)\lambda^{- 2}d\; \lambda}}$

where Λ denotes the range of wavelengths in the system.

The above equation determines the fractional concentration of basestates. It also advantageously corrects the previously measured fullspectra of the base states, {tilde over (σ)}_(open) and {tilde over(σ)}_(closed), to match the actual spectra in the device by applying thepreviously measured characteristics of the optical filters assembled inthe device, {tilde over (H)}_(sig) and {tilde over (H)}_(ref). Forexample,

σ_(sig,open,device) ={tilde over (H)} _(sig)(λ){tilde over(σ)}_(open)(λ)

is the effective spectrum of the open base state that is incident on thesignal channel of the device.

The above equation also calculates the power incident on thephotodetectors by numerically integrating the spectrum over the range ofwavelengths:

∫_(Λ) {tilde over (H)} _(sig)(λ){tilde over (σ)}_(open)(λ)λ⁻² dλ

This is the power that would be measured by the signal detector if allemitters were in the open state. The previously measured invariantreference is then computed for the previously measured spectra in asimilar manner to above:

∫_(Λ) {tilde over (H)} _(ref)(λ){tilde over (σ)}_(open)(λ)λ⁻² dλ

The reference, I_(ref), and the signal, I_(sig), are acquired from thedevice and the signal is normalized so that all spectra in the equationare based on the same factory-measured reference.

$I_{sig} \cdot \left\{ {\frac{1}{I_{ref}} \cdot {\int_{\Lambda}{{{\overset{\sim}{H}}_{ref}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}} \right\}$

The next step is to determine how the presence of glucose affects thefractional concentration of emitters, that is, how glucose concentrationdrives the equilibrium between the states. In the case of simple bindingof a ligand, G, to a protein, P,

P+G⇄P:G

the dissociation constant, K_(D), is given by

$K_{D} = \frac{\lbrack P\rbrack \lbrack G\rbrack}{\left\lbrack {P\text{:}G} \right\rbrack}$

Conversely, the equilibrium constant (also known as the associationconstant or affinity, K_(A)), K_(eq), is given by

$K_{eq} = {\frac{1}{K_{D}} = \frac{\left\lbrack {P\text{:}G} \right\rbrack}{\lbrack P\rbrack \lbrack G\rbrack}}$

In the case of one GBP binding one glucose molecule, the fractionalsaturation, Y, is the ratio of the moles of glucose bound to the molesof protein:

$Y = \frac{\left\lbrack {P\text{:}G} \right\rbrack}{\lbrack P\rbrack + \left\lbrack {P\text{:}G} \right\rbrack}$

which, by substituting and simplifying, results in:

$Y = {\frac{\lbrack G\rbrack}{K_{D} + \lbrack G\rbrack} = \frac{n_{closed}}{n_{closed} + n_{open}}}$

By further combining equations and solving for [G], the followingequation that solves for glucose concentration is obtained:

$\lbrack G\rbrack = {K_{D} \cdot \left\lbrack {\frac{I_{ref} \cdot {\int_{\Lambda}{\left( {{{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{closed}(\lambda)}} - {{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}}} \right)\lambda^{- 2}d\; \lambda}}}{{I_{sig} \cdot {\int_{\Lambda}{{{\overset{\sim}{H}}_{ref}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}} - {\int_{\Lambda}{{{\overset{\sim}{H}}_{sig}(\lambda)}{{\overset{\sim}{\sigma}}_{open}(\lambda)}\lambda^{- 2}d\; \lambda}}} - 1} \right\rbrack^{- 1}}$

The above equation is a hyperbolic function of the normalized signalintensity and a linear function of the dissociation constant, K_(D).

The optical filters and their transfer functions, H(A), are preferablycharacterized prior to use. As the signal and reference filters, H_(sig)and H_(ref), are defined as the net filters on that signal path, theyare preferably measured in conjunction with any common filters andtransfer functions in the system, that is, light source filter, detectorfilter, beam splitting dichroic, or spectra-altering reflectivecoatings. Characterization is preferably performed over wavelengths fromapproximately 380 nm to approximately 700 nm in steps of, for example, 1nm. Components are measured with the light incident on them at anglesequal to those used in the device. Several spectra are preferablymeasured for each base state in order to ensure stability and accuracyof measurements. The final functions, H(λ), are preferably stored foreach of the components in each OBS that uses that specific lot in itssensor.

Reference Band

Because real world filters cannot isolate a single frequency, it ispreferable to find a quasi-invariant reference band. This can berepresented as:

|∫_(Λ) H _(ref)(λ)σ_(open)(λ)λ⁻² dλ−∫ _(Λ) H _(ref)(λ)σ_(closed)(λ)λ⁻²dλ|<ε; ε>0

where ε is determined by the acceptable variation on the referencechannel.

As discussed above, there is a crossing in the base spectra. Thus thecontribution of each configuration to the intensity measured in thereference channel, I_(ref), is reversed about the crossing point,λ_(crossing). As the weighted average, σ_(total), changes from σ_(open)to σ_(closed), the contribution of I_(ref) will be monotonicallydecreasing in the range λ<λ_(crossing) and monotonically increasing inthe range λ>λ_(crossing). Accordingly, by virtue of the additivity ofoptical intensities and the linearity of the intergration operator, ifthere is a range [λ_(ref,min); λ_(ref,max)], such that

${\int\limits_{\lambda_{{ref},\min}}^{\lambda_{{ref},\max}}{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}} = {{\int\limits_{\lambda_{{ref},\min}}^{\lambda_{{ref},\max}}{{\sigma_{closed}(\lambda)}\lambda^{- 2}d\; \lambda}}:=}$

then the intensity measured over this range will be the same for allmixed configurations, that is, independent of the glucose concentrationin the sensor. In other words, as all spectra are a linear combinationof the base spectra, and as integration (power) is linear, it is onlynecessary to find the largest range that is maximally invariant betweenthe two base states. As the detected power increases with a broaderdetection range, the goal is to find as broad a passband as possiblethat meets the condition stated in the above equation, as this willmaximize the total detected power and increase the SNR of the referencechannel. This will also mitigate issued related to the numericalstability of dividing by a small number.

Referring to the data presented in FIG. 2, an optimal passband range wasdetermined to be from approximately 497 nm to approximately 617 nm.

${\int\limits_{497\mspace{14mu} {nm}}^{617\mspace{14mu} {nm}}{{\sigma_{open}(\lambda)}\lambda^{- 2}d\; \lambda}} = {{\int\limits_{497\mspace{14mu} {nm}}^{617\mspace{14mu} {nm}}{{\sigma_{closed}(\lambda)}\lambda^{- 2}d\; \lambda}}:={\neq {\lbrack G\rbrack}}}$

Using the preliminary data presented in FIG. 2, the difference betweenthe reference signals from each of the two base states was:

$\frac{{I_{{ref},{open}} - I_{{ref},{closed}}}}{I_{{ref},{open}}} = {\frac{{{2,240,235} - {2,240,267}}}{2,240,235} = {\frac{31.5}{2,240,235} = {{0.0014\%} \simeq 0}}}$

The level of variance found above is small enough to be consideredpractically invariant with respect to glucose concentrations.

Signal Band

It is preferable to find a passband to use as the signal channel thatwill maximize the total detected power and increase SNR. The signalchannel is also preferably maximally sensitive to any change in glucose.Because, as discussed above, all spectra are a linear combination of thebase spectra, and as integration (power) is additive, it is onlynecessary to find the largest range that is maximally changing betweenthe two base states.

|∫_(Λ) H _(sig)(λ)σ_(open)(λ)λ⁻² dλ−∫ _(Λ) H _(sig)(λ)σ_(closed)(λ)λ⁻²dλ|maximized

The data presented in FIG. 2 may be used to estimate this range. Theoptimal signal band was found to range from 415 nm, that is, the lowestwavelength available to the signal detector, to 521 nm=λ_(crossing),that is, the highest wavelength before the spectra reverse and changesin concentration begin to cancel each other out. The lower edge of thepassband is determined by the longest wavelength from the excitationsource that is allowed to enter the system in non-negligible amounts.Using preliminary data, the difference between the reference signalsfrom each of the two base states was:

$\frac{{I_{{ref},{open}} - I_{{ref},{closed}}}}{I_{{ref},{open}}} = {\frac{{{4,928,890} - {2,315,596}}}{4,928,890} = {\frac{2,613,294}{4,928,890} = {53\%}}}$

A series of graphs generated from the experimental set of spectrapresented in FIG. 1 will now be described. Each spectrum was acquiredthree times for each concentration level and averaged. The 0 mM glucoseand 30 mM glucose (not fully saturated, but the highest concentrationavailable for the analysis) were then integrated over all filter rangecombinations from 415 nm to 649 nm. Filters were assumed to be ideal,that is:

$\quad\left\{ \begin{matrix}{{{H(\lambda)} = 0},} & {\lambda < {{lower}\mspace{14mu} {limit}}} \\{{{H(\lambda)} = 1},} & {{{lower}\mspace{14mu} {limit}} \leq \lambda \leq {{upper}\mspace{14mu} {limit}}} \\{{{H(\lambda)} = 0},} & {\lambda > {{upper}\mspace{14mu} {limit}}}\end{matrix} \right.$

A comparison of this idealized filter with an actual optical filtermodel is shown in FIG. 3. The change in signal from 0 mM to 30 mM wasthen computed for each filter range by calculating the absolutedifference between the intensities at each of the two baseconcentrations. The optimal signal channel, H_(sig), will show thelargest change in signal over the range of concentrations. The optimalreference channel, H_(ref), will show negligible change over the rangeof concentrations. The optimal signal range was found to be from 415 nmto 521 nm and is limited at the low end by the emission spectrum of thelight source. The optimal reference range was found to be from 497 nm to617 nm.

FIG. 4 illustrates the change in measured signal strength intensitybetween two states of interest as a function of detection passbandconfigurations. An invariant passband which is suitable for use inreal-time calibration will exhibit negligible or no change with analyteconcentration. A strong signal will exhibit a large change with analyteconcentration. During the design and fabrication of the measurementdevice, the optimal passbands are determined for both the reference andthe signal channels. While in use, the signal is first treatedratiometically by dividing the signal intensity by the substantiallyinvariant reference intensity. This ratiometric operation is performedto normalize all signals to the reference signal, thereby ensuring thatall signals are interpreted on the same scale and in the same unitsacross devices and over the use of any single device. The normalizedsignal then serves as the basis for real-time calibration of the device.In exemplary embodiments of the invention, all three steps consisting ofratiometric measurement, normalization, and calibration are performedsimultaneously in one operation. This is substantially different fromconventional techniques whereby only some of the steps are performed,and preventing real-time calibration, or additional steps are added at alater stage to attempt calibration.

In FIG. 4, the axis representing the lower limit of an optical passbandis shown at 100. The axis 100 spans the range of wavelengths of interestin the system. The orientation of the axis is denoted by the verticalarrow in the frame. The axis representing the upper limit of an opticalpassband is illustrated at 101. The axis 101 spans the range ofwavelengths of interest in the system. The orientation of the axis 101is denoted by the horizontal arrow in the frame. The lower end 102 ofthe range of interest denotes the minima of axes 100 and 102. The upperend 103 of the range of interest denotes the maxima of axes 100 and 102.In area 104, the lower limits are greater than the upper limits, and aretherefore not applicable, so this area is blank. Example 105 is a narrowpassband at the lower end of the range of interest. Example 106 is anarrow passband at the upper end of the range of interest. Example 107is a passband that encompasses the entire range of interest. Example 108is a passband that spans the upper half of the range of interest. Point109 is the isosbestic or invariant point. Band 110 illustrates passbandsthat are invariant with respect to analyte concentration. Bands 111 and112 are passbands that have variability with respect to analyteconcentration but are sufficiently small to be considered essentiallyinvariant. Example 113 is an example of a passband specification chosenfor an embodiment as the calibration reference. Band 114 is a passbandthat exhibits maximal change with respect to analyte concentration. Area115 delimits the range of passbands that have significant change withrespect to analyte concentration. These have sufficiently large changeto be considered optimal signal passbands.

A process of lot calibration of selected components of a sensoraccording to exemplary embodiments of the present invention will now bedescribed in connection with FIG. 5. As illustrated, various componentsrelated to the optics and chemistry of the device are preferablycalibrated in lots at the factory or at the vendor. These components,shown in block 500, preferably include a signal filter 502, referencefilter 504, excitation/emission split 506, source filter 508, GBP at 0mM 510, GBP at saturation 512, and K_(D) 514. Calibration parametersrelated to each are preferably stored in the device, as shown in block516. As shown in block 518, in use the device reads a net signal 520 andnet reference 522 and determines auto-calibration data 524 for thedevice based on the net signal 520 and net reference 522. Glucoseconcentration is determined using self calibration 532 with input fromparameters stored in storage device 516 and auto-calibration data 524.Fractional states of GBP are determined at 534, and then bound glucoseis determined from the fractional states and K_(D) at 536. Lotcalibration advantageously eliminates the extensive device-levelcalibration and accordingly supports high-throughput manufacturing.Calculations are preferably performed real-time while in use to estimatethe glucose concentration inside the sensor.

Exemplary devices and methods for sensing glucose concentrationdescribed herein have significant advantages in performance,fabrication, and accuracy. Dynamic self-referencing to the invariantcrossing point advantageously corrects for photobleaching, excitationlight source variability (both nominal and drift), detector variation,coupling and alignment effects (including thermal), and optical filtervariation. Accordingly, this approach offers an exact and dynamiccalibration technology, which in turn produces a true self-referencingsystem.

The approach described herein guides and simplifies design, testing andcalibration of a device. The approach also enables automated real-timecalibration of the device in use.

Identifying optimal filter bands and storage of componentcharacteristics inside the device, as described herein, enable morerobust design. Indeed, much of the variability in the components can becharacterized in lot testing and accounted for in the equationsdescribed above. This advantageously results in a simpler, more robustdesign that uses fewer tight tolerance components, fewer customcomponents, a simplified assembly process, and simplified testing.

Although only a few embodiments of the present invention have beendescribed, the present invention is not limited to the describedembodiment. Instead, it will be appreciated by those skilled in the artthat changes may be made to these embodiments without departing from theprinciples and spirit of the invention.

What is claimed is:
 1. A diabetes management system comprising anoptical analyte sensor and an insulin infusion device, wherein theoptical analyte sensor comprises: a matrix for receiving a samplecontaining the analyte at an unknown concentration; a light emitter foremitting light at a stimulation frequency upon the sample; a lightreceiver for receiving a fluorescence signal at a first isosbesticfrequency, and at a second frequency, and for measuring an intensity ofthe fluorescence signal at the first and second frequencies; a processorfor determining a concentration of the analyte based on the respectiveintensities measured at the first and second frequencies; and whereinthe analyte sensor further comprises a transceiver for transmitting asignal to the insulin infusion device.
 2. The diabetes management systemof claim 1, wherein the processor further determines an insulinrequirement and wherein the signal transmitted to the insulin infusiondevice comprises an insulin requirement based on the determined insulinrequirement.
 3. The diabetes management system of claim 1, wherein thesensor is an in-vitro sensor.
 4. The diabetes management system of claim1, wherein the sensor is an in-vivo sensor.
 5. The diabetes managementsystem of claim 1, wherein the sensor is a continuous sensor.
 6. Thediabetes management system of claim 1, wherein the analyte is glucose.7. The diabetes management system of claim 1, wherein the analyte ishemoglobin HbA1c.
 8. The diabetes management system of claim 1, whereinthe analyte is glycated albumin.
 9. An optical analyte sensorcomprising: a matrix for receiving a sample containing the analyte at anunknown concentration; a light emitter for emitting light at astimulation frequency upon the sample; a light receiver for receiving afluorescence signal at a first isosbestic frequency, and at a secondfrequency, and for measuring an intensity of the fluorescence signal atthe first and second frequencies; a processor for determining aconcentration of the analyte based on the respective intensitiesmeasured at the first and second frequencies; wherein said processorfurther determines a sensor drift based on previous intensitymeasurements and corrects the determined concentration based on thedetermined sensor drift.
 10. The optical analyte sensor of claim 9,further comprising a transceiver for transmitting signals indicative ofdetermine analyte concentration to a remote device.
 11. The opticalanalyte sensor of claim 10, wherein the remote device is a smartphone.12. The optical analyte sensor of claim 10, wherein the transceivertransmits signals to a remote storage device.
 13. The optical analytesensor of claim 9, wherein the optical sensor comprises an energy sourceand is adapted for at least one day of continuous use.
 14. The opticalanalyte sensor of claim 9, wherein the optical sensor is used in thesubcutaneous space of a host.
 15. The optical analyte sensor of claim 9,wherein the optical sensor is used in the intradermal space of a host.16. The optical analyte sensor of claim 9, wherein the optical sensor isused in the supradermal space of a host.
 17. The optical analyte sensorof claim 9, wherein the optical sensor is used in the intravascularspace of a host.
 18. The optical analyte sensor of claim 9, wherein theoptical sensor is used in a bodily fluid.
 19. The optical analyte sensorof claim 9, wherein the optical analyte sensor is an in-vitro sensor.